Generalized projective synchronization between two different chaotic systems using active backstepping control

A novel active pinning control for synchronization and anti-synchronization of new uncertain unified chaotic systems

“…According to the idea of active control [8,9], we can use the control input u(t) to eliminate all items that cannot be shown in the form of the error e. By this way, the control input can be determined:…”

“…Various effective methods have been presented to synchronize various chaotic systems, for example, Lyapunov method, linear and nonlinear feedback control, adaptive control, impulse control, and so on [4][5][6][7][15][16][17]. G. Li proposed a generalized projective synchronization of two chaotic systems by using active control and active backstepping control [8,9]. X. Tan et al designed backstepping control to synchronize chaotic systems [10].…”

Stability and nonlinear controller design of Fast-Lock Phase-Locked Loop in 0.18-µm CMOS

“…The technique is based on generating a family of global asymptotically stabilizing control laws starting the design procedure by defining stable system and determining controller that gradually stabilize each outer subsystem. The process terminated when the external control is attained [11]. The method basically depends on applying Lyapunov functions in which guarantees the stability of the related system [12].…”

Recursive Backstepping Nonlinear Control and Sliding Mode Control of a Novel Hyperchaotic Finance System

“…Backstepping method has become one of the important and popular approaches for nonlinear systems [7][8][9]. The each two backstepping method employed in this paper has its own characteristics, but both effective.…”